An efficient analytical method for torsion analysis of open-section members of uniform thickness is presented. The conventional method based on the thin-walled theory for torsion analysis of bars can give good solutions only for members with small thickness and fillets of large radius. In the present method, a better approximation is employed, and much more accurate formulas are derived. The cross-section is considered to consist of some straight and curved (circular arc) segments. The Poisson equation of the torsion problem in terms of Prandtl's stress function is solved in each segment separately. By the present method, closed-form solutions for shear stress and torsional rigidity of members with open cross-section can be found. Some formulas for torsion analysis of tubes with a longitudinal slit and for members with angle and channel cross-section are derived. While these formulas are relatively simple, they give excellent results for thin- to moderately thick-walled members.